[tex]30a=24c\ \ \ \ \ |:30\\\\a=\dfrac{24}{30}c\\\\a=\dfrac{4}{5}c\\\\40b=\dfrc{24}{c}\ \ \ \ |:40\\\\b=\dfrac{24}{40}c\\\\b=\dfrac{3}{5}c[/tex]
substitute to a + b + c = 24
[tex]\dfrac{4}{5}c+\dfrac{3}{5}c+c=24\ \ \ \ |\cdot5\\\\4c+3c+5c=120\\\\12c=120\ \ \ |:12\\\\\boxed{c=10}\\\\a=\dfrac{4}{5}c\to a=\dfrac{4}{5}\cdot10=\to\boxed{a=8}\\\\b=\dfrac{3}{5}c\to b=\dfrac{3}{5}\cdot10\to\boxed{b=6}[/tex]
